Hierarchical structure formation in layered superconducting systems with multi-scale inter-vortex interactions

Abstract

We demonstrate formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and stripes in a cluster. We propose to realize such systems in vortex matter (where a vortex is mapped onto a particle with multi-scale interactions) in layered superconducting systems with varying inter-layer thicknesses and different layer materials.

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• Distinct magnetic signatures of fractional vortex configurations in multiband superconductors
• Mesoscale phase separation of skyrmion-vortex matter in chiral magnet-superconductor heterostructures
• Honeycomb, square, and kagomé vortex lattices in superconducting systems with multi-scale inter-vortex interactions
• Vortices with magnetic field inversion in noncentrosymmetric superconductors
• Hierarchies of Length Scale Based Typology in Anisotropic Multiband Superconductor
• Vortex chains due to nonpairwise interactions and field-induced phase transitions between states with different broken symmetry in superconductors with competing order parameters
• Phase diagrams of vortex matter with multi-scale inter-vortex interactions in layered superconductors
• Melting of a two-dimensional monodisperse cluster crystal to a cluster liquid
• Pinning effects in a two-dimensional cluster glass
• Cluster self-assembly condition for arbitrary interaction potentials
• Stripe Domains and First Order Phase Transition in the Vortex Matter of Anisotropic High-temperature Superconductors
• Ultrasoft classical systems at zero temperature
• Morse theory and Lescop's equivariant propagator for 3-manifolds with $b_1=1$ fibered over $S^1$